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Stochastic games with short-stage duration

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  • Abraham Neyman

Abstract

We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage $k$, $k\geq 0$, of a stochastic game $\Gamma_\delta$ with stage duration $\delta$ is interpreted as the play in time $k\delta\leq t 0}$ as the stage duration $\delta$ goes to $0$, and study the asymptotic behavior of the value, optimal strategies, and equilibrium. The asymptotic analogs of the discounted, limiting-average, and uniform equilibrium payoffs are defined. Convergence implies the existence of an asymptotic discounted equilibrium payoff, strong convergence implies the existence of an asymptotic limiting-average equilibrium payoff, and exact convergence implies the existence of an asymptotic uniform equilibrium payoff.

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  • Abraham Neyman, 2013. "Stochastic games with short-stage duration," Discussion Paper Series dp636, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp636
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    References listed on IDEAS

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    1. repec:dau:papers:123456789/6019 is not listed on IDEAS
    2. Yehuda Levy, 2013. "Continuous-Time Stochastic Games of Fixed Duration," Dynamic Games and Applications, Springer, vol. 3(2), pages 279-312, June.
    3. Solan, Eilon & Vieille, Nicolas, 2002. "Correlated Equilibrium in Stochastic Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 362-399, February.
    4. repec:eee:gamebe:v:104:y:2017:i:c:p:92-130 is not listed on IDEAS
    5. Eilon Solan & Rakesh V. Vohra, 2002. "Correlated equilibrium payoffs and public signalling in absorbing games," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 91-121.
    6. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.
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    Cited by:

    1. Fabien Gensbittel, 2016. "Continuous-time limit of dynamic games with incomplete information and a more informed player," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 321-352, March.
    2. Sylvain Sorin & Guillaume Vigeral, 2016. "Operator approach to values of stochastic games with varying stage duration," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 389-410, March.
    3. repec:spr:dyngam:v:8:y:2018:i:2:d:10.1007_s13235-017-0219-5 is not listed on IDEAS
    4. repec:eee:gamebe:v:104:y:2017:i:c:p:92-130 is not listed on IDEAS
    5. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications, Elsevier.
    6. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.

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